I don't think that's ever been studied.

I have seen papers about Downey Mildew being systemic in roses, even those that are asymptomatic.

I have in the past taken cuttings from a noisette that had a basal canker. The cane was a year old and I turned it into about nine four inch cuttings. The thinner ones didn't make it, but the pencil width cuttings did make good plants with no more proclivity to canker than the parent. So for that bush, it wasn't systemic.

If I were going to do it again, I'd toss the material two inches above the canker.

Right now, I'm seeing a lot of very early canker on my more modern roses. I think it's abnormally active this year because of the much warmer than ususal cold nights and the day times that are in the low 60s often enough to get the cankers jump started. I'm being especially picky with secateur cleanliness because I don't want to make a bad situation worse.

I would guess not, just leave good clearance above the canker as Ann says. You can take hardwood cuttings this time of year. Sometimes it works just to plant them in the garden with one bud eye exposed, not in full sun. See Kim's blog on "wrapping" hardwood cuttings, referred to in a thread on the Roses Forum.